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Cogito

Integrated Math 3 · Chapter 6 · Lesson 1

Practice Worksheet

The Pythagorean Identity

One equation the circle guarantees.

12 problems · about 21 minutes · F-TF.C.8

NameDate

Figure — use these to answer the problems

Move the angle and watch the two coordinates trade size while their squares still total 1.
(0.574, 0.819)
  • Angle55° = π/3 rad
  • x-coordinate0.574
  • y-coordinate0.819
  • cos 55°0.574
  • sin 55°0.819
Angle in degrees55
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. sin²θ = 0.64. What is cos²θ?

    Answer

  2. Where does the Pythagorean identity come from?

    • The unit circle equation x² + y² = 1.
    • It is an independent definition.

  3. sin²θ = 0.49. What is cos²θ?

    Answer

  4. cos θ = 0.8 with θ acute. What is sin θ?

    Answer

  5. What is sin²θ + cos²θ for any angle?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. tan²θ + 1 = 9. What is sec²θ?

    Answer

  2. cot²θ = 15. What is csc²θ?

    Answer

  3. sec²θ − tan²θ equals what number?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Match each expression with its simplest form.

    Draw a line from each item on the left to its match on the right.

    • One minus cos squared theta
    • One minus sin squared theta
    • sin theta over cos theta
    • sin squared theta
    • cos squared theta
    • tan theta

  2. sin²θ = 0.25. What is cos²θ?

    Answer

  3. The Square

    sin²θ = 0.36. What is cos²θ?

    Answer

  4. The Ratio

    sin θ = 0.6 with θ acute. What is cos θ?

    Answer